Yes, but not what you may be thinking. The AoA is the angle of the wing vs relative wind (the angle the wing is attacking the air). You can have high relative pitch (attitude) to the horizon but a low AoA, such as during climb. That same attitude is a full stall at slower speeds/power.
The wing doesn't care where the nose points. All it cares about is its relative angle to the wind. Once it diverges past a critical angle the wing stalls.
What appears to have happened with these MCAS issues is that the MCAS senses that the AoA is too high when it's completely normal and safe, so it auto-trims down.
The nose can be pointed up with a low angle of attack (e.g. a climb during cruise) and conversely the aircraft can be pitched down with a high angle of attack (e.g. descent approach with flaps extended)
What is your source? This is not what I have been reading. What I have been reading is that the MAX has a bigger engine and this engine has been positioned forward on the wing in order to preserve ground clearance. As a result of this unusual engine position, the MAX has a tendency to pitch up during acceleration. Nowhere did I read that this doesn't happen during normal flights.